I gather from your Original Post, that you need to come up with a δ, ε -proof.

So, given an arbitrary ε > 0, you need to show that there is a δ ( which usually depends upon ε ) such that for any x, in the domain of f, that satisfies 0 < |x - 0| < δ, it's true that |f(x) - L|< ε. In this case L = 0.